Skip to main content
SpringerLink
Log in

New unsteady boundary layers over a long thin cylinder

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

In this paper, a new family of unsteady boundary layers over a long cylinder was investigated. This new class of unsteady boundary layers involves the flows over a long thin cylinder, whose leading end is either accretion or ablation at a certain rate. Using dimensionless variables, the governing partial differential equations are transformed into an ordinary differential equation, which was solved with a shooting method numerically. Under special cases, the solution can be solved explicitly. Solution domain was estimated and calculated numerically. It is found that a unique solution exists for accretion, while two solutions can exist for ablation. For other ablation parameters, there are no solutions. This new type of unsteady boundary layers over a cylinder enriches the literature on flow passing a cylinder and can provide benchmark problems for validating numerical code of computational fluid dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Smith FT (1986) Steady and unsteady boundary layer separation. Annu Rev Fluid Mech 18:197–220

    Article  ADS  Google Scholar 

  2. White FM (1991) Viscous fluid flow, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  3. Schlichting H, Gersten K (2000) Boundary Layer Theory, 8th revised and enlarged edition (English). Springer, New York

    Book  Google Scholar 

  4. Ludlow DK, Clarkson PA, Bassom AP (2000) New similarity solutions of the unsteady incompressible boundary layer equations. Q J Mech Appl Math 53(2):175–206

    Article  MATH  MathSciNet  Google Scholar 

  5. Ma PH, Hui WH (1990) Similarity solutions of the two dimensional unsteady boundary layer equations. J Fluid Mech 206:537–559

    Article  MathSciNet  ADS  Google Scholar 

  6. Yang KT (1958) Unsteady laminar boundary layers in an incompressible stagnation flow. Trans ASMEJ Appl Mech 25:421–427

    MATH  Google Scholar 

  7. Todd L (1997) A family of laminar boundary layers along a semi-infinite flat plate. Fluid Dyn Res 19:235–249

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Fang T (2008) A note on the unsteady boundary layers over a flat plate. Int J Nonlin Mech 43:1007–1011

    Article  Google Scholar 

  9. Batchelor GK (1954) The skin friction on infinite cylinders moving parallel to their length. Q J Mech Appl Mech 7:179–192

    Article  MATH  MathSciNet  Google Scholar 

  10. Glauert MB, Lighthill MJ (1955) The axisymmetric boundary layer on a long thin cylinder. Proc R Soc Lond Ser A Math Phys Sci 230(1181):188–203

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Sakiadis BC (1961) Boundary layer behavior on continuous solid surfaces: III. The boundary layer on a continuous cylindrical surface. AICHE J 7(3):467–472

    Article  Google Scholar 

  12. Crane LJ (1972) Boundary layer flow on a circular cylinder moving in a fluid at rest. J Appl Math Phys (ZAMP) 23:201–212

    Article  MATH  Google Scholar 

  13. Curle SN (1980) Calculation of the axisymmetric boundary layer on a long thin cylinder. Proc R Soc Lond Ser A Math Phys Sci 372:555–564

    Article  MATH  ADS  Google Scholar 

  14. Eshghy S, Hornbeck RW (1967) Flow and heat transfer in the axisymmetric boundary layer over a circular cylinder. Int J Heat Mass Transf 10:1757–1766

    Article  MATH  Google Scholar 

  15. Richelle E, Tasse R, Riethmuller ML (1995) Momentum and thermal boundary layer along a slender cylinder in axial flow. Int J Heat Fluid Flow 16:99–105

    Article  Google Scholar 

  16. Crane LJ, McVeigh AG (2011) Accelerated slip flow past a cylinder. A Angew Math Phys 62:365–378

    Article  MATH  MathSciNet  Google Scholar 

  17. Tutty OR (2008) Flow over a long thin cylinder. J Fluid Mech 602:1–37

    Article  MATH  ADS  Google Scholar 

  18. Wolfram S (1993) Mathematica: a system for doing mathematics by computer, 2nd edn. Addison-Wesley Publishing Company Inc, New York

    Google Scholar 

  19. Drazin P, Riley N (2006) The Navier–Stokes equations: a classification of flows and exact solutions (London Mathematical Society Lecture Note Series 334). Cambridge University Press, New York

    Book  Google Scholar 

  20. Seban RA, Bond R (1951) Skin friction and heat transfer characteristics of a laminar boundary layer on a cylinder in axial incompressible flow. J Aeronaut Sci 18(10):671–675

    Article  MATH  Google Scholar 

  21. Kelly HR (1954) A note on the laminar boundary layer on a circular cylinder in axial incompressible flow. J Aeronaut Sci 21:634

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The author would like to thank the anonymous reviewers for their constructive comments and suggestions to improve the paper.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, North Carolina State University, 3246 Engineering Building III, 911 Oval Drive, Campus Box 7910, Raleigh, NC, 27695, USA

    Tiegang Fang

Authors
  1. Tiegang Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tiegang Fang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fang, T. New unsteady boundary layers over a long thin cylinder. Meccanica 50, 2907–2918 (2015). https://doi.org/10.1007/s11012-015-0177-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-015-0177-1

Keywords

Search

Navigation